A377458 - OEIS

%I #37 Dec 13 2024 09:40:25

%S 1,1,1,4,7,29,61,256,596,2507,6247,26197,68652,286232,780508,3231060,

%T 9102590,37392935,108279767,441342883,1308552478,5292781266,

%U 16018989626,64315663716,198213843417,790252270626,2474924176566,9802205324516,31142246753638

%N G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^4).

%F a(n) = (1/n) * Sum_{k=0..n} (-1)^k * binomial(n,k) * binomial(2*n-4*k,n-k-1) for n > 0.

%o (PARI) a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(2*n-4*k, n-k-1))/n);

%Y Cf. A317133, A364759, A377706, A378958, A378920.

%Y Cf. A371891.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Dec 12 2024